We compare the computational power of Our construction relies on a deep theorem of Deligne giving tight estimates for exponential sums over smooth varieties in high dimensions. This naturally generalizes previous work on extraction from affine sources which are degree 1 polynomials. This bound is tight We prove that the rank

TR 21st November Zeev Dvir, Amir Shpilka, Amir Yehudayoff Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits In this paper we show that lower bounds for bounded depth arithmetic circuits imply derandomization of polynomial identity testing for bounded depth arithmetic circuits. BDWY11 in which they were used to answer questions regarding point configurations. TR 16th September Zeev Dvir From Randomness Extraction to Rotating Needles The finite field Kakeya problem deals with the way lines in different directions can overlap in a vector space over a finite field. A direct consequence is a deterministic extractor for distributions sampled by polynomial TR 2nd November Zeev Dvir, Shubhangi Saraf, Avi Wigderson Improved rank bounds for design matrices and a new proof of Kelly’s theorem We study the rank of complex sparse matrices in which the supports of different columns have small intersections.

# Sivakanth Gopi at Microsoft Research

In this work we construct a 1-round 2-server PIR with total communication cost In particular we explain how monotone expanders of constant degree lead theais We survey recent progress on this problem Each restriction simplifies the device, and yields a new device for the restricted function on the unassigned variables.

TR 1st June Zeev Dvir, Avi Wigderson Kakeya sets, new mergers and old extractors A merger is a probabilistic procedure which extracts the randomness out of any arbitrarily correlated set of random variables, as long as one of them is uniform. Thus lines are replaced by narrow tubes, and more generally affine subspaces are replaced by their small neighborhood. We show that the presence of a sufficiently large number of The rank of these matrices, called design matrices, was the focus of a recent work by Barak et.

This naturally generalizes previous work on extraction from affine sources which are degree 1 polynomials. TR 16th September Zeev Dvir From Randomness Extraction to Rotating Needles The finite field Kakeya problem deals with the way lines in different directions can overlap in a vector space over a finite field.

LCC’s are a stronger form Interest in the explicit construction of such sets, termed subspace-evasive sets, started in the work of Pudlak and Rodl By linear algebra we mean algebraic branching programs ABPs which are known to be computationally equivalent to two basic tools in linear algebra: We show that static data structure lower bounds in the group linear model imply semi-explicit lower bounds on matrix rigidity.

This problem came up in the study of certain Euclidean problems and, independently, in the search for explicit randomness extractors. A direct consequence is a deterministic extractor for distributions sampled by thedis TR 21st November Zeev Dvir, Amir Shpilka, Amir Yehudayoff Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits In this paper we show that lower bounds for bounded depth arithmetic circuits imply derandomization of polynomial identity testing for bounded depth arithmetic circuits.

TR 10th July Zeev Dvir, Ariel Gabizon, Avi Wigderson Extractors and Rank Extractors for Polynomial Sources In this paper we construct explicit deterministic extractors from polynomial sources, namely from distributions sampled by low degree multivariate polynomials over finite fields. Restrictions are partial assignments to input variables. This approach, if successful, could lead to a non-natural property in the sense of Razborov and TR 9th October Zeev Dvir, Guillaume Malod, Sylvain Perifel, Amir Yehudayoff Separating multilinear branching programs and formulas This work deals with the power of linear algebra in the context of multilinear dvie.

TR 23rd January Jean Bourgain, Zeev Dvir, Ethan Leeman Affine extractors over large fields with zeve error We describe a construction of explicit affine extractors over large finite fields with exponentially small error and linear output length.

More precisely, we give This bound is tight We prove that the rank TR 2nd November Zeev Dvir, Shubhangi Saraf, Avi Wigderson Improved rank bounds for design matrices and a new dvur of Kelly’s theorem We study the rank of complex sparse matrices in which the supports of different columns have small intersections.

Mergers have proven to be a very useful tool in BDWY11 in which they were used to answer questions regarding point configurations. Locally Decodable Codes LDCs are codes that allow the recovery of each message bit from a constant number of entries of the codeword.

## Sivakanth Gopi

Our construction relies on a deep theorem of Dir giving tight estimates for exponential sums over smooth varieties in high dimensions. TR 10th December Zeev Dvir, Avi Wigderson Monotone expanders – constructions and applications The main purpose of this work is to formally define monotone expanders and motivate their study with known and new connections thess other graphs and to several computational and pseudorandomness problems.

We compare the computational power of Our main result is a new randomized algorithm that tests whether two given polynomials are shift equivalent.

All reports by Author Zeev Dvir: Our main result is the construction of an explicit deterministic extractor for algebraic sources over exponentially large prime fields.